We must mention here, most of these problems addressed into the light for an asymptotically flat spacetimes but the current observation shows that our universe is going through an accelerated phase. So its natural to ask how this information paradox problem gets affected in presence of a positive cosmological constant \(\Lambda \) . Summing it up, we are interested here in the information paradox problem of stationary black hole with a positive cosmological constant \(\Lambda \)  or the Schwarzschild de-Sitter black
hole spacetime. This problem become significant since these black holes can be thought to formed during the early inflationary phase of our universe e.g.,[1]}, [2]}, [3]}, [4]} and keeping in mind the current phase of accelerated expansion of our universe, it also provide a nice toy models for the global structures of isolated black holes of our universe. Also much like the case of black holes, in de-Sitter space there exist causally disconnected regions. So an observer can only gain access to the parts of the universe which is bounded by its respective horizon. As a whole the Schwarzschild de-Sitter black hole spacetime have two event horizon, the cosmological event horizon (CEH) and the black hole event horizon (BEH), while the cosmological event horizon serve as the global causal boundary of the de-Sitter spacetimes. Both of these event horizon posses different temperature thermodynamics compare to \(\Lambda \le 0\)  single horizon spacetime  [5]}, [6]}, [7]}. Similar to the black hole, cosmological event horizons emits and absorb radiation (Gibbons-Hawking radiation). Loosely speaking, compare to the black hole, entropy generation of the cosmological horizon is an observer dependent property and it gets generated due to the ignorance about what lies beyond the cosmological horizon.
